210205A Francisco Javier Martinez Aguinaga

February 5, 2021

Title: Flexibility in contact 3-manifolds: From contactomorphisms to legendrian knots

Speaker: Francisco Javier Martinez Aguinaga (Junior talk, 4:30pm)

The study of the homotopy type of the space of legendrian submanifolds in a contact manifold is a central problem in Contact Topology. In this talk, mimicking the techniques developed in Smooth Knot Theory (work of A. Hatcher and R. Budney), we will relate the homotopy type of such spaces with the homotopy type of the contactomorphism group of the complement.

In particular, we show that the inclusion of each connected component of the space of long legendrian embeddings into the space of smooth long embeddings is a homotopy equivalence. This result shows that, except for the number of connected components, the homotopy of the space of Legendrians is governed by the topology of the space of smooth knots.

This talk will be the first part of a 2-talk session, followed by "On the homotopy type of the contactomorphism group of a tight contact 3-manifold" by Eduardo Fernández. Joint work with Eduardo Fernández and Francisco Presas.

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